th

Capillary tubes are widely used as expansion device in small scale refrigeration systems.

isobutane

ielle

Although capillary tubes have been used as expansion device

of the vapor refrigeration cycle especially in small scale sys-

tems like household refrigerators or small air conditioning

systems formany decades, to design a capillary tube for a given

refrigeration cycle is still amost empirical and time consuming

enomena inside the

us pressure drop and

evaporation of the refrigerant, an analytic and explicit

description of the total throttling process is not possible.

Therefore many attempts have been done to develop simple

design methods in the past. These design methods always

imply certain simplifications or assumptions and must be

* Corresponding author. Tel.: 49 721 608 42730.

Available online at www.sciencedirect.com

e:

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0E-mail address: schenk@kit.edu (M. Schenk).Mots cles : Tube capillaire adiabatique ; R600a ; Resultats experimentaux ; Ecoulement amorti ; conception factor

1. Introduction process. Due to the complex flow phcapillary tube, caused by the simultaneoEtude experimentale de lecoulement du frigorige`ne(R600a) dans des tubes capillaires adiabatiquesArticle history:

Received 27 June 2013

Received in revised form

29 August 2013

Accepted 31 August 2013

Available online 9 September 2013

Keywords:

Adiabatic capillary tube

R600a

Experimental results

Factorial design

Choked flow0140-7007/$ e see front matter 2013 Elsevhttp://dx.doi.org/10.1016/j.ijrefrig.2013.08.024Despite the simple geometry one finds complex physical processes during the throttling in

the capillary tube, which were subject of many studies in the last decades. However, there

is currently only one source of experimental data for the refrigerant isobutane (R600a) and

adiabatic capillary tubes (Melo et al., 1999). In order to close this gap a test rig was built and

experimental data in the range of typical small scale refrigeration systems was collected.

The measured mass flow rates span from 0.64 kg h1 to 1.93 kg h1. Additionally, the effect

of critical flows (Choked Flow) is shown by means of an extra performed test. The semi-

algebraic equation from Hermes et al. (2010) showed a remarkable level of agreement by

predicting 94% of all points within a 10% error band. 2013 Elsevier Ltd and IIR. All rights reserved.a r t i c l e i n f o a b s t r a c tof isobutane (R600a) through adiabatic capillarytubes

Matthias Schenk*, Lothar R. Oellrich

Karlsruhe Institute of Technology (KIT), Institute for Technical Thermodynamics and Refrigeration, Engler-Bunte-

Ring 21, 76131 Karlsruhe, GermanyExperimental investigation of

www. i ifi i r .org

journal homepagier Ltd and IIR. All rightse refrigerant flow

www.elsevier .com/locate/ i j refr igreserved.

validated with experimental data. The experiments must al-

ways be done in the same range as the design method is going

to be used. Especially in the case of Isobutane (R600a), which is

nowadays a commonly used refrigerant in small scale refrig-

eration systems, there is only one source of experimental data

available (Melo et al. (1999) and reviewed by Khan et al. (2009)).

Up tonowonly 19data pointshavebeenpublished,where in

all experiments the same inner diameter was used. The tests

were donewith high condensation pressures (7.1e11.3 bar) and

high mass flow rates were measured (2e4 kg h1). Both pa-rameters are much higher than the usual conditions in typical

small scale refrigeration systems. Thispaper aims to extend the

2. Experimental work

Nomenclature

D inner diameter (m)

L length of capillary tube (m)_M mass flow rate (kg s1)p pressure (Pa)

T temperature (C)DTsub subcooling degree (

C)v specific volume (m3 kg1)

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 02762.1. Experimental setup

Fig. 1 shows the scheme of the workbench which was built

and used to perform the presented tests. The workbenchavailable database for R600a and adiabatic capillary tubes to

lower mass flow rates and check the validity of existing design

methods proposed in the literature in this range. First results

were already published in (Schenk and Oellrich, 2012).Fig. 1 e Scheme of the workbench.basically represents a simple vapor-compression refrigeration

cycle. The compressor is a 9 cm3 hermetic variable velocity

compressor, whose frequency range spans from 20 to 75 Hz. In

order to avoid oil contamination in the test section, the

refrigerant passes through one oil separator and two oil filters

with 0.01 mm as smallest filtering element particle size. Both

oil separator and filters are supplied with electrical heaters

that are used to eliminate the risk of refrigerant condensation.

In order to control the high-side pressure, a proportional

valve is placed after the compressor. With the valve the mass

flow rate to the condenser can be regulated. The condenser is

a fan supplied tube-and-fin heat exchanger using an electrical

heater to set up the air temperature at the entrance. There-

fore, the capillary tube inlet pressure, i.e. the condensation

pressure, can be set through the valve opening, heater power

and fan frequency control.

After the condenser the liquid refrigerant flows through a

subcooler consisting of several Peltier elements attached to a

copper block embedding the refrigerant tube. The subcooled

liquid flows through a Coriolis mass flow meter. Next, a filter

dryer is used to hold back humidity or impurities that could

clog the capillary tube. The inlet temperature of the capillary

tube is controlled by an electrical preheater. In a sight glass

after the preheater and prior to the capillary tube inlet one can

check for the presence of bubbles in the refrigerant flow.

The inlet and outlet temperatures are measured with

mineral insulated K-type thermocouples, each 0.5 mm in

diameter, whose probes are positioned directly in the flow.

The inlet pressure is measured using a piezoresistive pressure

transducer. After the capillary tube the refrigerant enters the

tubular evaporator equipped with an electrical heater. The

power of the heater can be adjusted to ensure that only su-

perheated vapor exits the evaporator. Then the refrigerant

flows back to the compressor.

All pressure transmitters and thermocouples were cali-

brated before the measurements. The coriolis mass flow

Greek Letters

r density (kg m3)

F capillary constant (6.0)

Subscripts

in inlet to the capillary tube

out outlet of the capillary tube

f entrance in the two-phase domain

s saturation statemeter was calibrated by the manufacturer. The inner diam-

eter of the capillary tubes was determined by means of mi-

croscope pictures. Short pieces of the capillary were welded

into a copper block and afterward the surface of the block was

milled and polished. The flow area on the pictures was

marked and calculated with appropriate software. Doing this

at several points before and after the tested capillary tube, the

equivalent inner diameter was obtained. All the uncertainties

of the measurements are listed in Table 1.

The stated purity of the refrigerant by the manufacturer

was 98.5% isobutane. The refrigerant was filled into the cycle

from the liquid phase. Also the measured temperature in the

two-phase flow after the capillary tube corresponded with the

planning of the tests (Box et al., 2005). For all available test

this fact an extra test was performed where all parameters

2.4. Experimental results

In Table 4 the results of all test runs (Design of Experiments

and additional tests) are listed. The values of DTsub were

calculated with the equation for the vapor pressure given in

Bucker and Wagner (2006). In all tests the outlet pressure was

set below the critical pressure for the choked flow occurrence

(see Section 2.3) by adapting the compressor frequency. The

its implementation demand a high degree of time and effort.

Table 2 eMinimum and maximum values for the Designof Experiments.

Parameter () () Physical unitpin 4.5 6.0 bar (minuscules)

DTsub 8.0 13.0C

D 0.69 0.61 mm

L 2.5 3.9 m

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0 277were kept constant with the outlet pressure continuously

lowered during 4.5 h from 2.2 bar to 0.6 bar. Fig. 2 shows theparameters a minimum and maximum value were fixed: (1)

the inlet pressure pin, (2) the subcooling degree at the capillary

inlet DTsub, (3) the inner diameter D and (4) the length L of the

capillary tube. The chosen minimum and maximum values

are given in Table 2. These values are combined in a scheme in

away that all possible combinations are each reproducedwith

one run, which results in a total amount of 42 16 test runs.The scheme is shown in Table 3.

Because the individual test runs of this scheme combine

always the edges of the operating range (e.g. the highest

condensation pressure together with the biggest diameter),

very high subcooling degrees were chosen to avoid two phase

flow at the capillary tube entrance.

To broaden the scope of the presented data, also tests with

a lower subcooling at the capillary entrance and additional

three different capillary tubes (tests 17e22 in Table 4) were

performed.

2.3. Choked flow

As can be seen in Section 2.2 the outlet pressure was not

considered as a parameter in the design of experiments, due

to its marginal influence on the mass flow rate. To illustratecalculated saturation temperature of the measured pressure

and thus indicated a pure refrigerant.

2.2. Design of experiments

In order to cover the complete scope of conditions of small

scale refrigeration systems with a minimal amount of test

runs, the Two-level Factorial Design method was used for the

Table 1 e Uncertainties of the measurements.

Measured parameter Uncertainty

Temperature 0.2 CPressure 5 mbarMass flow rate 1%Inner diameter 0.01 mmCapillary tube length 5 mmresulting mass flow rate versus the outlet temperature of the

capillary tube.

The very small instabilities of the inlet pressure, which

resulted in a standard deviation over all points in these 4.5 h of

only 15 mbar, were noticeable on the enlarged scale of the

mass flow rate. In order to point out the effect of the inlet

pressure fluctuations, all data points for which the deviation

of the inlet pressure to itsmean valuewaswithin the standard

deviation are printed as filled circles. The other points are

presented as empty circles.

Fig. 2 clearly illustrates, that the mass flow rate does not

change anymore as the outlet pressure falls below 1.3 bar.

This is the range of Choked Flow.Additionally the discretisation of the process brings up

Table 3 e Scheme for the two-level factorial design (Boxet al., 2005).

Test pin DTsub D L

1 2 e Low Pressure Control Valve was kept fully open in all tests.

3. Comparison with available correlations

Due to the drastic change of the fluid properties in the two-

phase flow along the capillary tube, it is not possible to

describe the throttling process with analytical and explicit

equations. In order to obtain a reliable tool for the design of

capillary tubes in spite of these difficulties the following ap-

proaches evolved during the last decades:

3.1. Finite-volume based methods

Following the finite-volume based methods the capillary tube

is divided into single cells and the fluid properties are aver-

aged over these cells. Thus an accurate description of the

process is obtained. However, the creation of the model and3 e 4 e e 5 e 6 e e 7 e e 8 e e e 9 e10 e e11 e e12 e e e13 e e14 e e e15 e e e16 e e e e

Table 4 e Experimental results.

Test pin/bar Tin/C Tout/C L/m

Tests from the Design of Experiments e scheme

1 6.02 32.0 19.9 3.932 4.52 21.0 21.3 3.933 6.04 37.0 21.7 3.934 4.49 26.0 21.3 3.935 6.02 32.0 23.2 3.936 4.53 21.0 25.3 3.937 6.02 37.0 24.2 3.938 4.51 26.0 21.5 3.939 6.00 31.9 16.7 2.4910 4.50 21.0 19.5 2.4911 6.02 37.0 15.4 2.4912 4.48 26.0 20.3 2.4913 6.01 32.0 20.6 2.5314 4.50 21.0 25.9 2.5315 6.02 37.0 20.6 2.5316 4.50 26.1 24.7 2.53Additional tests

17 4.10 27.7 19.5 2.7318 5.30 34.1 21.9 2.7319 5.30 37.0 19.6 2.7920 4.00 23.7 11.2 2.7921 4.00 27.0 26.7 4.0422 5.29 34.0 25.9 4.04

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0278numerical issues one has to handle (Melo et al., 1992). Exam-

ples of this approach are given in Bansal and Rupasinghe(1998), Li et al. (1990) or Garca-Valladares et al. (2002).

Because of the named drawbacks this approach is not

further followed up in this work.

-30 -20 -10 0 101,20

1,22

1,24

1,26

1,28

1,30pin inside (5.0 +/- ) barpin outside (5.0 +/- ) bar

M/(

kgh-

1 )

Tout / C

0,5 1,0 1,5 2,0 2,5

pS(Tout) / bar

Tin = 27C =0.06 Kpin = 5.0 bar =0.015 bar

Choked Flow

Fig. 2 e Illustration of choked flow.3.2. Empirical correlations

D/mm DTsub/C pSTout/bar _M/(kg h1)

0.692 12.9 0.73 1.535

0.692 13.0 0.69 1.379

0.692 8.0 0.67 1.340

0.692 7.7 0.69 1.280

0.611 12.9 0.63 1.104

0.611 13.0 0.58 0.846

0.611 7.8 0.61 1.000

0.611 7.9 0.68 0.831

0.692 12.8 0.83 1.920

0.692 12.8 0.74 1.689

0.692 7.8 0.88 1.773

0.692 7.7 0.72 1.400

0.611 12.8 0.71 1.457

0.611 12.8 0.56 1.183

0.611 7.8 0.71 1.265

0.611 7.8 0.59 1.098

0.607 2.8 0.74 0.807

0.607 5.9 0.67 1.079

0.617 2.9 0.74 0.964

0.617 5.8 1.04 0.873

0.610 2.6 0.54 0.645

0.610 5.9 0.56 0.932Another approach is represented by empirical correlations,

which focus on the applicability of the method. Most often

empirical correlations are developed with the Buckingham-Pi-

Theorem (dimensional analysis). Thereby all variables which

are considered to have an influence on themass flow rate and

are independent from each other are combined in dimen-

sionless groups. These groups are fitted by means of an

appropriate equation form (mostly power-law) to measure-

ment data. Another method to develop empirical correlations

came up in the last years applying neural networks to find an

adequate equation form to fit the empirical parameters to

experimental results.

Shao et al. (2013) reviewed 20 empirical correlations for the

prediction of the mass flow rate through adiabatic capillary

tubes and compared the agreement of eleven representative

correlations with 182 experimental data points of different

sources, comprising five different refrigerants. Only data

which was not used for the development of the investigated

correlation was chosen for the comparison. Thus, due to the

lack of independent experimental data for R600a, the authors

could not check the validity of the correlations for this

refrigerant.

The recommendation of the review from Shao et al.

resulted in the correlation from Yang and Zhang (2009). This

correlation was developed with a neural network approach

and represents an expansion of an earlier work (Zhang and

Zhao, 2007) in order to also cover super critical flow of CO2.

The authors used 710 experimental data points with capillary

tube flow, including the results for R600a of Melo et al., to train

the neural network, i.e. to find an adequate equation form. In

within an error band of 15% is reported.

able, the capillary constantF, (Hermes et al., 2010). A fit on 761

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Measured mass flow rate / (kg h )-1

+10%

-10%

Melo et al. (1999)This work

Pred

icte

d m

ass

fl ow

rat

e /(k

g h-1

)

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0 279As Fig. 3 shows the empirical correlation from Yang and

Zhang predicts both the experimental results of Melo et al. as

well as our own points on R600a systematically by about 20%

too high.

3.3. Algebraic equationsthe paper a prediction of all 710 training data points of 93%

Fig. 3 e Prediction of the experimental data through the

correlation of Yang and Zhang (2009).Several scientists tried to develop an analytical description of

the capillary tube flow by introducing simplifying

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Pred

icte

d m

ass

flow

rat

e /(k

g h- 1

)

Measured mass flow rate / (kg h-1)

-10%

Melo et al. (1999)This work +10%

Fig. 4 e Prediction of the experimental data by Hermes

equation (Hermes et al., 2010).in-house data points with R134a and R600a resulted in a value

F 6.

_M FD5

L

"pin pf

vf pf pout

a ba2

ln

a pout ba pf b

!#vuut (1)

The parameters a and b, which represent fitting parameters

for the description of the specific volume in the two phase

domain, were adopted fromZhang andDing (2004) and Yilmaz

and Unal (1996) accordingly, where a vf 1 k, b vfpf k andk 1:63,105p0:72f . It is worth mentioning that the parameter kshould be dimensionless, but is not. In order to arrive at cor-

rect results Pascal as the physical unit of the pressure has to

be implemented.

The authors report an agreement of Equation (1) with their

experimental results of 89%within the aimed10% error band(Hermes et al., 2010). In case of R600a the database comprised

189 data points obtained from two different tube lengths with

one single inner diameter. The mass flow rate varied between

2 kg h1 and 4 kg h1 (about 150 We300 W refrigerationcapacity).

In Fig. 4 the experimental results of this work and the

published data of Melo et al. (1999) is compared with the re-

sults of the Hermes equation. As can be seen, the equation

also predicts the mass flow rates in the range from 0.65 kg h1

to 2 kg h1 covered in this work verywell. Out of the Design ofExperiments e scheme only one point lies outside the 10%

error bands. In total a prediction of 94% of both datasets

within an 10% error band is achieved.

4. Conclusions

The presented experimental results extend the published

database for R600amass flow rates through adiabatic capillary

tubes in the range of flow rates from 0.65 kg h1 to 2.0 kg h1. Atest rig was constructed which allows to measure the mass

flow rates through different capillary tubes under controlled

boundary conditions. By means of the statistical method

Factorial Design the complete range of small scale refrigera-

tion systems was covered with 16 tests. Additionally the re-

sults of sixmore tests, with lower subcooling of the refrigerant

at the capillary inlet and three additional capillary tubes, areassumptions for the calculation of the fluid properties along

the capillary tube. In this way they were able to transform the

governing differential equations into their integral form. They

obtained an algebraic equation which can predict the mass

flow rate or alternatively the geometry of the capillary tube for

given boundary conditions. Although empirical parameters

are included in these equations, too, they are based on a

physical background.

One of the first successful attempts on this field was the

one by Yilmaz and Unal (1996). This work was continued by

Zhang and Ding (2001, 2004) and Yang and Wang (2008). In

2010 Hermes et al. published an algebraic Equation (1) in

which all the empirical parameters are merged in one vari-reported. The comparison of existing correlations for adia-

batic capillary tubes and the experimental data produced a

good level of agreement with the semi-algebraic equation of

Hermes et al. from 2010.

Acknowledgments

We thank the students Adriano Ronzoni and Bruno Yuji

Kimura de Carvalho for their great help with the experimental

work within their project work at ITTK.

r e f e r e n c e s

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Experimental investigation of the refrigerant flow of isobutane (R600a) through adiabatic capillary tubes1 Introduction2 Experimental work2.1 Experimental setup2.2 Design of experiments2.3 Choked flow2.4 Experimental results

3 Comparison with available correlations3.1 Finite-volume based methods3.2 Empirical correlations3.3 Algebraic equations

4 ConclusionsAcknowledgmentsReferences